Modern Defense Technology ›› 2026, Vol. 54 ›› Issue (3): 93-103.DOI: 10.3969/j.issn.1009-086x.2026.03.009
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Tongyu SHI1, Hao WANG2, Youkun WANG1, Maolong LÜ1
Received:2025-05-28
Revised:2025-08-21
Online:2026-06-28
Published:2026-07-03
Contact:
Maolong Lü
通讯作者:
吕茂隆
作者简介:史桐雨(2004-),男,河南南阳人。本科生,研究方向为有人无人协同空战。
CLC Number:
Tongyu SHI, Hao WANG, Youkun WANG, Maolong LÜ. Simulation of Game-Theoretic Decision-Making for Beyond-Visual-Range Combat with UCAVs[J]. Modern Defense Technology, 2026, 54(3): 93-103.
史桐雨, 王昊, 王酉琨, 吕茂隆. 无人作战飞机超视距空战博弈对抗决策仿真[J]. 现代防御技术, 2026, 54(3): 93-103.
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| A | 介绍 | A | 介绍 |
|---|---|---|---|
| a1 | 直飞加速 | a7 | 半滚倒转防御 |
| a2 | 爬升 | a8 | 大回环防御 |
| a3 | 目标位置追踪 | a9 | 90°侧转机动 |
| a4 | 高强度回旋 | a10 | 置尾机动 |
| a5 | 低强度回旋 | a11 | 策略偏置 |
| a6 | 高角度追踪 | a12 | 蛇形机动 |
Table 1 Tactical action based on the decision frame of beyond visual range air combat
| A | 介绍 | A | 介绍 |
|---|---|---|---|
| a1 | 直飞加速 | a7 | 半滚倒转防御 |
| a2 | 爬升 | a8 | 大回环防御 |
| a3 | 目标位置追踪 | a9 | 90°侧转机动 |
| a4 | 高强度回旋 | a10 | 置尾机动 |
| a5 | 低强度回旋 | a11 | 策略偏置 |
| a6 | 高角度追踪 | a12 | 蛇形机动 |
| Q | 介绍 |
|---|---|
| q1 | 远距离对峙(我方飞机距离敌方≥30 km) |
| q2 | 中远距离对峙(距离<30 km而≥10 km) |
| q3 | 中近距离对峙(距离<10 km而≥5 km) |
| q4 | 近距离对峙(距离<5 km) |
| q5 | 低能量状态(高度速度过低) |
Table 2 Typical situation of beyond visual range air combat decision frame
| Q | 介绍 |
|---|---|
| q1 | 远距离对峙(我方飞机距离敌方≥30 km) |
| q2 | 中远距离对峙(距离<30 km而≥10 km) |
| q3 | 中近距离对峙(距离<10 km而≥5 km) |
| q4 | 近距离对峙(距离<5 km) |
| q5 | 低能量状态(高度速度过低) |
| E | 介绍 | E | 介绍 |
|---|---|---|---|
| e1 | 天线偏置角变化 | e3 | 导弹锁定告警 |
| e2 | 能量评估 | e4 | 高度速度评估 |
Table 3 Typical events of the decision frame of beyond visual range air combat
| E | 介绍 | E | 介绍 |
|---|---|---|---|
| e1 | 天线偏置角变化 | e3 | 导弹锁定告警 |
| e2 | 能量评估 | e4 | 高度速度评估 |
| C | 介绍 |
|---|---|
| c1 | 我方飞机能量<目标能量的0.6倍 |
| c2 | 天线偏置角>70° |
| c3 | 天线偏置角≤15° |
| c4 | 天线偏置角>120°且进入角>150° |
| c5 | 距离<300 m且天线偏置角>60° |
| c6 | 天线偏置角>30° |
Table 4 Typical conditions of beyond visual range air combat decision frame
| C | 介绍 |
|---|---|
| c1 | 我方飞机能量<目标能量的0.6倍 |
| c2 | 天线偏置角>70° |
| c3 | 天线偏置角≤15° |
| c4 | 天线偏置角>120°且进入角>150° |
| c5 | 距离<300 m且天线偏置角>60° |
| c6 | 天线偏置角>30° |
| Rule | Q | E | C | A | Q' |
|---|---|---|---|---|---|
| Rule1 | q1 | e1 | c2 | a3 | q2 |
| Rule2 | q1 | e1 | ¬c2 | a11 | q1 |
| Rule3 | q2 | e1 | c3 | a12 | q3 |
| Rule4 | q2 | — | — | a3 | q2 |
| Rule5 | q3 | e2 | c1 | a1 | q3 |
| Rule6 | q3 | e1 | c4 | a4 | q4 |
| Rule7 | q3 | e1 | c6 | a5 | q4 |
| Rule8 | q3 | e3 | — | a9 | q4 |
| Rule9 | q3 | — | — | a3 | q3 |
| Rule10 | q4 | e1 | c6 | a3 | q4 |
| Rule11 | q4 | e1 | c4 | a7 | q4 |
| Rule12 | q4 | e1 | ¬c4⋁¬c5⋁¬c6 | a6 | q4 |
| Rule13 | q4 | e1 | c5 | a8 | q4 |
| Rule14 | q4 | e3 | — | a10 | q4 |
| Rule15 | q4 | e4 | — | a2 | q1 |
| Rule16 | q5 | — | — | a2 | q1 |
Table 5 Decision frame rule set for beyond visual range air combat
| Rule | Q | E | C | A | Q' |
|---|---|---|---|---|---|
| Rule1 | q1 | e1 | c2 | a3 | q2 |
| Rule2 | q1 | e1 | ¬c2 | a11 | q1 |
| Rule3 | q2 | e1 | c3 | a12 | q3 |
| Rule4 | q2 | — | — | a3 | q2 |
| Rule5 | q3 | e2 | c1 | a1 | q3 |
| Rule6 | q3 | e1 | c4 | a4 | q4 |
| Rule7 | q3 | e1 | c6 | a5 | q4 |
| Rule8 | q3 | e3 | — | a9 | q4 |
| Rule9 | q3 | — | — | a3 | q3 |
| Rule10 | q4 | e1 | c6 | a3 | q4 |
| Rule11 | q4 | e1 | c4 | a7 | q4 |
| Rule12 | q4 | e1 | ¬c4⋁¬c5⋁¬c6 | a6 | q4 |
| Rule13 | q4 | e1 | c5 | a8 | q4 |
| Rule14 | q4 | e3 | — | a10 | q4 |
| Rule15 | q4 | e4 | — | a2 | q1 |
| Rule16 | q5 | — | — | a2 | q1 |
| 参数名称 | 数值 |
|---|---|
| 初始距离/km | 100~120 |
| 初始高度/km | 8~10 |
| 初始Ma数 | 1.0~1.2 |
| 初始方位角/(°) | 150~180 |
| 挂载近距弹数量 | 2 |
| 挂载中距弹数量 | 3 |
Table 6 Initialization data of simulation experiment environment
| 参数名称 | 数值 |
|---|---|
| 初始距离/km | 100~120 |
| 初始高度/km | 8~10 |
| 初始Ma数 | 1.0~1.2 |
| 初始方位角/(°) | 150~180 |
| 挂载近距弹数量 | 2 |
| 挂载中距弹数量 | 3 |
| 类型 | 中距弹发射数 | 近距弹发射数 | 胜率/% |
|---|---|---|---|
| 红方 | 2.7 | 1.8 | 17 |
| 蓝方 | 2.5 | 1.5 | 71 |
Table 7 Average arithmetic data of simulation experiment
| 类型 | 中距弹发射数 | 近距弹发射数 | 胜率/% |
|---|---|---|---|
| 红方 | 2.7 | 1.8 | 17 |
| 蓝方 | 2.5 | 1.5 | 71 |
| 参数 | 介绍 |
|---|---|
| 我方战机三维坐标 | |
| 我方战机速度矢量 | |
| 敌方战机三维坐标 | |
| 敌方战机速度矢量 | |
| 敌我距离矢量 | |
| 天线偏置角 | |
| 尾后角 | |
| 我与敌导弹距离矢量 |
Table 8 State space input information parameters
| 参数 | 介绍 |
|---|---|
| 我方战机三维坐标 | |
| 我方战机速度矢量 | |
| 敌方战机三维坐标 | |
| 敌方战机速度矢量 | |
| 敌我距离矢量 | |
| 天线偏置角 | |
| 尾后角 | |
| 我与敌导弹距离矢量 |
| A | 介绍 | A | 介绍 |
|---|---|---|---|
| a1 | 直飞加速 | a6 | 高角度追踪 |
| a2 | 爬升 | a7 | 半滚倒转防御 |
| a3 | 目标位置追踪 | a8 | 大回环防御 |
| a4 | 高强势回旋 | a9 | 蛇形机动 |
| a5 | 低强势回旋 | a10 | 三九机动 |
Table 9 Action space tactical action set
| A | 介绍 | A | 介绍 |
|---|---|---|---|
| a1 | 直飞加速 | a6 | 高角度追踪 |
| a2 | 爬升 | a7 | 半滚倒转防御 |
| a3 | 目标位置追踪 | a8 | 大回环防御 |
| a4 | 高强势回旋 | a9 | 蛇形机动 |
| a5 | 低强势回旋 | a10 | 三九机动 |
| 奖励类型 | 事件 | 取值 |
|---|---|---|
| 回合奖励 | 胜 | 10 |
| 平 | 0 | |
| 负 | -8 | |
| 击落 | 2 | |
| 被击落 | -2 | |
| 关键事件奖励 | 锁定 | 0.05 |
| 被锁定 | -0.05 | |
| 规避导弹 | 1 | |
| 导弹未命中 | -1 | |
| 优势态势奖励 | 能量优势 | 0.05 |
| 高度优势 | 0.04 | |
| 角度优势 | 0.03 | |
| 高度保护 | 安全飞行 | 0.005 |
| 危险飞行 | -0.5 | |
| 单步奖励 | 每步 | -0.01 |
Table 10 Reward function event and value design
| 奖励类型 | 事件 | 取值 |
|---|---|---|
| 回合奖励 | 胜 | 10 |
| 平 | 0 | |
| 负 | -8 | |
| 击落 | 2 | |
| 被击落 | -2 | |
| 关键事件奖励 | 锁定 | 0.05 |
| 被锁定 | -0.05 | |
| 规避导弹 | 1 | |
| 导弹未命中 | -1 | |
| 优势态势奖励 | 能量优势 | 0.05 |
| 高度优势 | 0.04 | |
| 角度优势 | 0.03 | |
| 高度保护 | 安全飞行 | 0.005 |
| 危险飞行 | -0.5 | |
| 单步奖励 | 每步 | -0.01 |
| 评估维度 | 指标名称 | 规则集 | 状态机转移 |
|---|---|---|---|
| 对抗效能 | 胜率/% | 70.8 | 78.0 |
| 武器使用 | 单目标命中所需发射数 | 1.9 | 1.7 |
决策 能力 | 威胁识别准确率/% 战术响应延迟/ms | 91.1 240 | 92.7 233 |
| 鲁棒性 | 策略迁移成功率/% | 89 | 83 |
Table 11 Simulation experiment data statistics
| 评估维度 | 指标名称 | 规则集 | 状态机转移 |
|---|---|---|---|
| 对抗效能 | 胜率/% | 70.8 | 78.0 |
| 武器使用 | 单目标命中所需发射数 | 1.9 | 1.7 |
决策 能力 | 威胁识别准确率/% 战术响应延迟/ms | 91.1 240 | 92.7 233 |
| 鲁棒性 | 策略迁移成功率/% | 89 | 83 |
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